What do you think of someone like this? Do you think he's just so smart that it's pointless to expect him to have ordinary human motivations and thus uninteresting to understand why he's doing this? Do you admire him for this, and if you do, why? It has to have meaning to be admirable, doesn't it? Or do you find it beautifully poignant, like weeding a desert?

The prospect of being awarded a Fields Medal had forced him to make a complete break with his profession. “As long as I was not conspicuous, I had a choice,” Perelman explained. “Either to make some ugly thing” — a fuss about the math community’s lack of integrity—“ or, if I didn’t do this kind of thing, to be treated as a pet. Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit.” We asked Perelman whether, by refusing the Fields and withdrawing from his profession, he was eliminating any possibility of influencing the discipline. “I am not a politician!” he replied, angrily. Perelman would not say whether his objection to awards extended to the Clay Institute’s million-dollar prize. “I’m not going to decide whether to accept the prize until it is offered,” he said.

Mikhail Gromov, the Russian geometer, said that he understood Perelman’s logic: “To do great work, you have to have a pure mind. You can think only about the mathematics. Everything else is human weakness. Accepting prizes is showing weakness.” Others might view Perelman’s refusal to accept a Fields as arrogant, Gromov said, but his principles are admirable. “The ideal scientist does science and cares about nothing else,” he said. “He wants to live this ideal. Now, I don’t think he really lives on this ideal plane. But he wants to.”

He could be just smart in that now he may logically expect to stand head and shoulders above the other three recipients of the Field Medal. This translates into more money and fame, both motivators of people. Indeed, he seems to be less risk averse than the capitalists in general.

Most likely it has to do with way his brain is wired and very little to do with normal motivations. Math geniuses at this level have a high incidence of what is probably Asperger's syndrome demonstrating poor social skills, no ability to see how they affect others, and avoidant behaviors. Bobby Fischer was the same way.

It would be unethical for me to place such a diagnosis on Dr. Perleman without interviewing him, but there is a long and well documented history of such diagnoses in high level mathematicians. I doubt that wealth and fame are considerations in this case.

I smell real-politik in this case. It would be interesting to read about the experience of his family in WWII and his current relationship with Putin and the Russian Intelligence agency. People like Grigory Perelman have an interesting history that motivates them.

Time well tell. If we do not hear from him again, we will know his desire to not be in the forefront was genuine and had an opportunity cost in excess of $1M.

If we start to hear constantly about him, we know that he has excellent PR skill or handlers who recognize the cachet of being able to "selflessly turn down $1M" as creditentials that he is something different.

But my first thought was that he had been reading the suggestions on how to be a better evil overlord. http://www.eviloverlord.com/lists/overlord.html

The reason I'm not a Math PhD student is because (a) not smart enough, (b) not crazy enough, (c) not compulsive enough. Oh, and I can't juggle to save my life.

Computational and applied math types are everyday normal people. To excel at theoretical math, I think you need to be at least slightly autistic. (Like Gauss, for example) At those levels, I think doing math is its own reward.

Maybe he cares so much about math that he believes that accepting a prize for his offering to the discipline he loves would be somehow tawdry. Prof. A would know more about this, but it seems like an attitude that an artist might adopt, for example.

I'm no psychiatrist, but the high-level mathematicians I know are just...not like the rest of us. Not crazy, necessarily, but they just don't seem to view the world like the rest of us.

It's really exciting that much of the Field-medal-winning math is being done at the boundary of math and physics. On the physics side, we have a series of problems which our current math cannot describe, or describes very clumsily, and we often use computer simulation rather than find analytical solutions. Like Newton or Dirac, we've had to resort to making up our own math as we go along. It's nice to see the much more rigorous mathematicians doing some of the heavy lifting for us.

Perelman may be interested in fame, but if so he probably seeks a different kind of fame than what we would commonly recognize. And solving the Poincare Conjecture is a Big Deal. His fame is assured, even if no one besides family, friends and colleagues recognize him on the street. Long after Madonna and Michael Jackson and Prince are forgotten, someone will still be studying his results, trying to apply them to new and interesting problems.

What do I think of him? I wish I had his drive and ability! This article makes me wish I hadn't given up on my mathematics career to become a faceless financial number-cruncher, but I never had the talent to see the world as he does. Alas....

As for his decisions, I can only take him at his word that he is taking a principled stand. No background is given as to why he feels isolated from the mathematical community at large, but others in the community seem sympathetic. Pride can can overcome greed as a motivation, this I can understand.

Regardless, Perelman has pushed the boundaries of human accomplishment, and deserves the accolades even if he refuses them.

Altoids, whenever I hear about string theory or dark matter or dark energy or the standard model, I feel uneasy. It seems like too much is being added to the theoretical models in an ad hoc fashion. I can't help but feel that we're just waiting for another genius like a Newton or Einstein to come along and explain to the rest of us that we just are pictuing the Universe in the wrong way. We need another genius!

Interesting guy, silly debate. Is it really at all meaningful or useful to speculate about the guys motivations, or the place along the socialite spectrum a subjective evaluation of his 'wiring' would place him? Earlier articles and commentary from colleagues during his post-doctoral phase suggest Perelman has always been a bit of a recluse. Apparently he used to talk quite animatedly about walking for hours in the woods, hunting mushrooms; but otherwise was largely silent on matters not related to math. He probably doesn't see the point of the money. As for his being 'so smart that it's pointless' that sounds rather silly - doesnt it? He's just not firmly embedded in any mainstream social fabric, so his take on what it means to exist is probably a little bit different.

It is entirely possible that Perelman views prizes as part of a competetive system, and simply rules himself out of any such enterprise. It wouldn't be so surprising. The pursuit of mathematics, especially at the rarefied levels that Perelman inhabits, calls for a great deal of austerity in many aspects of his life. Part of cultivating that austerity is to shun everything that is not necessary to the pursuit of one's intellectual goals. Perelman might have discarded many social affectations along the way. I do not find his rejection bizarre or strange at all. We are used to grandiose, grandstanding academics. Perelman just happens to be different. Lets respect his choice, and welcome the diversity that he introduces into this picture.

It is entirely possible that Perelman views prizes as part of a competetive system, and simply rules himself out of any such enterprise. It wouldn't be so surprising. The pursuit of mathematics, especially at the rarefied levels that Perelman inhabits, calls for a great deal of austerity in many aspects of his life. Part of cultivating that austerity is to shun everything that is not necessary to the pursuit of one's intellectual goals. Perelman might have discarded many social affectations along the way. I do not find his rejection bizarre or strange at all. We are used to grandiose, grandstanding academics. Perelman just happens to be different. Lets respect his choice, and welcome the diversity that he introduces into this picture.

Well gee, maybe there are people in the world who are motivated by things other than money, fame and power. Maybe they are just satisfied by the discovery and knowledge! What a shocking concept.

How can anything be more important than money or the pursuit of money? It's just impossible. Isn't that the highest goal of mankind?

Once you accept the fact the concept that the money is meaningless to him (he has enough to fulfill all his needs, why could he possibly want more), then the only issue is why he has turned down the prize. Again, he solved the problem, everybody knows it, why does he need the stupid prize and hassle with all the travel and getting dressed up in a tux and all that other nonsense? He would rather pick mushrooms.

He lives in a world of pure mental energy and abstraction. He is probably not even aware half the time that he is eating or tying his shoes or going to the bathroom, or what time he goes to work or leaves work or maybe even what day it is. Such things are a waste of energy. We need to read Dune and consider the 'beings' who did the navigation and folded time in order to get a better appreciation of this fellow. His only mirth in life is his hobby, and we all have at least one. He may find a bit of pleasure on rare occasions picking up odd shaped, odd colored rocks when he happens to be outdoors. I suspect he collects string and rolls it into a ball and secretly chuckles knowing that the world does not know that such a genius would do such a thing.

I started out as a math major, but by sophomore year knew that a career in math wasn't for me. At any good university, there will always be a few students each year who are truly gifted in pure math. Before I got to college, I thought I was a real math wiz. But merely getting a top score on the SAT (it was 800 back then, but that may have changed) meant nothing -- it was quite a shock to learn that, measured by their scale, I could never be better than mediocre at best. I met several such math geniuses, and as individuals they were very strange indeed, as were some of the professors.

Most of them were classic loners, like Perelman. They had their world, and it tended to be a private one -- populated by proofs and concepts, all expressed in a language closed to all but the cognoscenti. It wasn't so much that they were dysfunctional socially, although social awkwardness was a common trait, but instead that math was a very jealous mistress (every truly gifted math student I met was a male). Also like Perelman, they couldn't have cared less about their clothes, money wasn't a big motivator, and even personal hygiene would sometimes get lost in the shuffle. But when they talked about what attracted them to math, words like "beauty" and "simplicity" often came up. In a way, the pursuit of math at that level was an aesthetic exercise. They were artists consumed by the desire to understand, and maybe someday to create, an abstract construct that rendered simple, clear and concise what had previously been confusing and complex; that laid out the deep connections that united and made one what had previously been separate and disconnected. It was a Platonic idea of Beauty that outsiders were unlikely to relate to. It wasn't surprising that an intense interest in music was also a common denominator.

I suspect that anyone who ever pursued a career in pure math will recognize Perelman as a not-so- unusual personality type in that field. I don't think Perelman necessarily lacks "ordinary human motivations," but rather that he finds satisfaction and fulfillment of very common desires in an uncommon way. Given how he lives, he has no need for or any apparent interest in obtaining large amounts of money. And he is already famous -- he doesn't need a medal for that. I think he is interested in a more lasting fame, and regards his peers as the true giants of his chosen field across the ages -- David Riemann, Gauss, Poincare, Fermat, to name a few. If there were a pantheon were he could be installed as one of them, he might be interested. But that can only be achieved by the lasting value of his work -- no medal can do that (just scan a list of Nobel winners, to see how many are forgotten today). Instead only time will tell.

Reading this reminds me of my favorite musician, Glenn Gould (also posthumously "diagnosed" with Asperger's Syndrome by some) who also believed in (and practiced) a life of isolation from the incidental activities of his profession. He gave up doing concerts at the height of his career, never performing before an audience again, and devoted the rest of his short life to recording; because of this, he made a much greater and more lasting contribution to music than other musicians who spent their life concertizing. Because he didn't waste his best years in that way, we now have his greatest work available to us in his recordings, his television programs and his wonderful documentaries on such far-afield subjects as Canadian Mennonites and Arnold Schoenberg.

My favorite film director, Stanley Kubrick, was also like this. It's the path of the greatest minds.

Yah, I'm aware of the mystery of the missing Universe. It's just that the dark matter/dark energy stuff just sounds so arbitrary. Personally I feel like we just don't understand the basic geometry of the Universe. (Of course, my personal feeling on the matter don't mean squat!) Perhaps Perelman's work can help in this regard....

OTH, the standard model is rock-solid science. Used and tested everyday, for at least three decades. Proven to at least 5-8 decimal points. It doesn't get anymore certain than this.

Whoops, I thik I mis-wrote earlier. I didn't mean the Standard Model of Partical Physics (SMPP). I meant the Standard Model of Cosmology. (See here.) But it's been so long since I followed this stuff even in a lay-man's fashion that I don't even know if the SMC is still accepted terminology or accepted theory.

The Super-Conducting Super Collider! That was hot stuff back when I was in high school--too bad they cut the funding for it. It's now a huge, underground mushroom farm, if I've heard correctly. How sad.

Are we that selfish? Is it possible to accept his work graciously, as a gift?Giving him the Fields medalis a just acknowledgment of his gift. Now, we are asking him to earn our admiration by his acceptance of our acknowledgement, with humility, of course.

It's interesting that according to the book "A Beautiful Mind" John Nash was very much motivated by competitiveness and a hunger for fame, and his frustration at being unable to solve a Fields Medal-quality problem contributed significantly to his mental illness.

I hope I didn't come off as being snarky, that wasn't my intent, but anyways...

It's a real shame the SSC was cancelled. I wasn't old enough to realize it at the time it was canceled, but without the SSC or some replacement, the future of particle/high-energy physics will be in Europe. I'm have no idea if it would be powerful to test string theory, but it's generally true that every time we test a higher energy, we discover something new. But it's to hard to get the average politican to understand this. The SSC wasn't pork.

About the standard model - hmm, maybe things were different in your day, but as far as I know, the words "standard model" always refers to particle physics.

Great Post!Just adding in that many high SAT scores are not from true top end genius but maximizing what gifts you have through perserverence and hard work. I went the other direction...slacker, National Merit Scholar semi-finalist, US Marine Corps, Masters, Gulf War doing nothing really, PhD at 41!

Which only made me, like 800 SATs Richard Dolan, smart enough to understand the chasym between MENSA-hood level brains and the steep infinite but rare part of the upper elements of the Bell Curve/

But in my days, I got to work with a few, and am so convinced by the few gifted that have such advanced capabilities that I think evolution is poising for a new human leap...

That said, there is stereotyping, in many ways useful, but not when it "defines" people like USMC, mathematicians.

Like with Mikeyes - Math geniuses at this level have a high incidence of what is probably Asperger's syndrome demonstrating poor social skills, no ability to see how they affect others, and avoidant behaviors. Bobby Fischer was the same way.

It would be unethical for me to place such a diagnosis on Dr. Perleman without interviewing him, but there is a long and well documented history of such diagnoses in high level mathematicians. I doubt that wealth and fame are considerations in this case.

That sounds like Frist's diagnosis of Teri Schiavo being as aware and cognitive of her surroundings as Frist.

My own observations are of a cowboy Sri Lankan PhD mathemetician who broke his arm at an amateur rodeo and bass fished with us with a rod he rigged to operate one-handed 4 days later saying Sri Lankans are no pussy-men, and a former German lover and lifelong friend with a PhD in Applied Math and Particle Physics - who loves to come to the USA and sledgehammer rocks for crystals while her husband & kids hit "Waterworld". Who is well-liked by my family as "Tina and her Swiss husband Henrique", who work with atoms at CERN" and had our daughter Rachel live with them and boosted up to finish 7th in her grade in Bavaria despite being in US public schools beforehand and a year behind her German and Swiss classmates when she started. "T" is beyond whip-smart, but like her equally whip-smart husband and kids...top-notch folks! Life's like that.

Some geniuses are totally normal once they leave university work areas - perhaps given "genius moments" and dispensation now and then. "Oh my God I get it!" serendipity moments in the oddest circumstances when you know they should run with it and indulge. But gys and gals who get wild at Bon Jovi concerts, show they are...ummm..hot companions in a particular time! And years later bring other great folks back as welcome new buddies and with new awesome kids. Husband totally cool around a former BF of hers, even a former Texan USMC officer dude - maybe only because of no Alpha Male challenges to him to mock knife combat or bayonet drills - just good times. (Their son caught a monster alligator snapping turtle last visit that was 43 pounds and mean, so f**king mean - but at least 80 pictures of the turtle and the Swiss canton 2nd highest 6th grade science student with his monster, handing over his monster to a black maestro cooking family (Dad's a oilwell owner but a homey) so we all could dine on 1 1/2 gallons the of the son of genius's "Soul Snapper Stew". the young fisher-hunter called it..and check my German..."potthassliches schnappschildekrot suppe".

Her husband has the Max Planck Research Prize. She may get "reflected Nobel luster" for her 80s work in some quantum thing that I am 40-70 IQ points under "Tina" in grasping.

Both fit into America far better than we do as visitors to Karlseruhe or Switzerland. Though I had Swiss marveling at my USA fly fishing skills and in awe of my wife showing how Texan women rule in ANY dance.

Altoids, you didn't come off as snarky at all, and I'm sorry if I gave that impression. Thanks for the interesting comments.

It appears that the SMC is not widely accepted terminology. I'm not even sure where I heard/read about it first, but there do seem to be a few references to it out there. I had know about the SMPP, but had completely forgot about it! I really really miss the academic life. Business just sucks my mind dry....

Not so incidentally, the New Yorker piece makes it clear why Perelman is refusing the Fields Medal. Basically, a sharp bureaucratic operator is trying to screw Perelman and steal credit for the solution. Sad but true: there are a lot of bastards in the mathematical community.

I was not trying to stereotype math geniuses, but offering one possible explanation. Frist's explanations about Terry Shiavo were strictly politics and a violation of medical ethics. I wanted to make it clear that it would be unethical to place that explanation for his refusal on a distant diagnosis.

My information comes from both the book an Paul Erdos and experience with this illness and with savants of all kinds (I have a partner who is a world expert on the subject.) It is possible that math geniuses can be normal appearing people with normal interests and pursuits, I know a few, but there are other explanations that can be offered without the PC police attending to the issue.

Bringing up Asperger's Syndrome is more for information than to place a stigma on Prof Perlman. But at that end of the bell curve, there are many fascinating and different minds that are hard to explain using normal paradigms. The chances of savant minds being different from, say, mine, is fairly high, but not a certainty.

What if you read that Beethoven had accepted the Best Composer Alive award for his ninth symphony? Personally I'd find it somehow unworthy of such an immortal work, and his acceptance of it understandable - human, but altogether irrelevant and just a bit embarassing.

It is clear that Perelman did not decline the prize in response to any particular controversy or trauma. His original paper was simply posted to the internet and never submitted for peer review.

It is almost certain that Perelman knew immediately his solution was correct (for such things do not happen accidentally.) His proof is unconventional, hugely imaginative, and is of magnificent importance not just to mathematics but to physicists working on String Theory, potentially the Theory of Everything.

He joined the pantheon of intellectual immortals the moment he clicked Submit on his paper. The polite applause of envious colleagues, it is easy to imagine, is an all too mortal anticlimax.

There was a brief scuffle over priority as some of his peers allegedly tried to take credit for the work. Perleman ignored the controversy and was vindicated in absentia.

To glimpse, for the first time in human history, something beautiful, something important, something eternal - is a very rare experience and we cannot pretend to grasp how it feels. I imagine Perleman observed the fight for the prize with a sense of "What fools these mortals be."

His proof is the prize.

Rumor has it he is now working on String Theory. In secret, because all this attention is simply distracting.